To solve the equation \( -3 - |6 - 3x| + 7 = 4 \), we can start by simplifying the left side.
Combine the constants: \[ -3 + 7 = 4 \] So, the equation simplifies to: \[ 4 - |6 - 3x| = 4 \]
Next, isolate the absolute value: \[
- |6 - 3x| = 4 - 4 \] \[
- |6 - 3x| = 0 \]
Since the absolute value is always non-negative, the only way this equation holds true is if: \[ |6 - 3x| = 0 \]
This implies: \[ 6 - 3x = 0 \] Solving for \( x \): \[ 6 = 3x \] \[ x = \frac{6}{3} = 2 \]
Now, we can verify that \( x = 2 \) satisfies the original equation by substituting it back: \[ -3 - |6 - 3(2)| + 7 = -3 - |6 - 6| + 7 \] This leads to: \[ -3 - 0 + 7 = 4 \] \[ 4 = 4 \]
Thus, \( x = 2 \) is indeed a solution.
The final answer is: \[ \boxed{2} \]